MONTE CARLO, Monaco – Just before noon on a brilliant Riviera day, two columns of guards line up smartly in front of the Prince's Palace, gold braid glinting on their full dress uniforms, vivid blue helmets rivaling the azure sky.

A bell tolls as the guards put on what may be the world's most glamorous shift change, marching and presenting arms with practiced precision as a crowd of tourists standing just feet away Instagram the moment.

The best part? Watching this piece of royal pageantry won't cost you a sou.

Sure, Monaco's known as the "millionaire's playground," and it's easy to see why, from the multimillion-dollar penthouses and high-roller casinos to the fleets of Bentleys and Ferraris roaming the narrow streets. But you don't have to break the bank at Monte Carlo to have fun in Monaco. Here are some things to do that will cost you as much as Monegasques (as the locals are called) pay in income tax. Which is to say, zero.

DRIVE

Monaco is a principality covering less than 1 square mile (2.6 square kilometers) on the French Riviera, near Nice. (If you're car-less, you can get here by the No. 100 bus from Nice for under $2.) Set on a narrow strip of land bordered by France on three sides and the Mediterranean on the other, Monaco can be reached by three scenic roads, the Basse Corniche (low coast road), the Moyenne Corniche (middle coast road) and the Grande Corniche (great coast road). Fans of the Hitchcock classic "To Catch a Thief" may recognize the Grande Corniche as one of the roads Grace Kelly and Cary Grant drive along. Tragically, Kelly, who famously married Monaco's Prince Rainier and became Princess Grace of Monaco, died in a car crash near the Grande Corniche in 1982.

A key stop on your Monaco visit is the Prince's Palace in Monaco-ville, the old city perched on a rocky promontory known, logically, as Rocher de Monaco or "the Rock." At 11:55 a.m. each day you can see the changing of the guard on the square in front of the palace; http://www.palais.mc . Line up early if you want a good view; this is popular. In winter, the guards wear dark uniforms, in summer, white. As you walk into the square, look for the statue of Francesco Grimaldi, who dressed as a monk to lead a surprise raid on the castle in the 13th century.

After you're done with the guards, follow the signs to the Monaco Cathedral nearby. Here you'll find the tombs of past members of the ruling Grimaldi family including those of Prince Rainier and Princess Grace (4 rue Colonel Bellando de Castro; free admission outside of religious services 8:30 a.m.-7 p.m., 6 p.m. in winter).

Another must-see is the Monte Carlo Casino. (Monte Carlo is one of 10 districts within Monaco.) Going into the gaming room will cost you 10 euros and, incidentally, you'll need to be well-dressed and carrying a passport to show you're not a Monaco resident since they are banned. But it costs nothing to walk around the lobby, with its marble flooring, columns, sculptures and pictures; http://www.montecarlocasinos.com , open from 2 p.m. daily.

Also free, taking a picture beside one of the posh cars to be found parked outside the ornate, Belle Epoque building. Check out the sculpture, "Sky Mirror," facing the casino, a large, circular mirror that reflects the building and nearby Café de Paris.

STROLL

Home to about 32,000 people, Monaco is largely urban. But there are a number of parks that provide green oases where you can stop to smell the flowers or rest up on a convenient bench. The St. Martin Gardens, just below the Monaco Cathedral, are nice to walk in after you've visited that building; 2 Avenue Saint Martin. http://www.visitmonaco.com/en/Places-to-visit/Gardens/St-Martin-Gardens . Come here for views of the Mediterranean and check out the statuary, including a larger-than-life rendition of Albert I as a navigator looking out to sea.

Another good place to find respite is the Japanese Garden not far from the Monte Carlo Casino. Inspired by Zen Buddhism, the garden includes a waterfall and stream; Avenue Princesse Grace, open 9 a.m.-sunset, http://www.visitmonaco.com/en/Places-to-visit/Gardens/JapaneseGarden2 .

PACE

You're going to need a rather expensive car, along with a few other requirements, to compete in the Grand Prix de Monaco held in May. But walking the course the rest of the year? That's not going to cost you a dime. Stop by the Monaco tourism center, 2a Boulevard des Moulins, to pick up a free map of the route, a circuit of approximately 2 miles (3.2 kilometers). The route passes the Monte Carlo Casino, the famous hairpin turn in front of the Fairmont, formerly the Loews Hotel Monte-Carlo, and the bottom half of the circuit hugs the coast with views of yacht-studded harbors.

STAMP

There's no border checkpoint to pass through when visiting Monaco. But if you want an official memento of your visit, you can get your passport stamped at the tourism office, a short walk from the Monte Carlo casino. A cut above the bland insignias of many countries, the stamp is of the Monaco coat of arms which features two sword-wielding monks in honor of the wily Francesco Grimaldi.

Maybe you'll go home feeling as cunning as old Francesco. After all, you've sampled the gilded streets of Monaco without parting with a copper.